Hello sage-gsoc! My name is Simon Spicer; I am a 4th-year mathematics PhD candidate at the University of Washington in Seattle (although I originally hail from South Africa), working under William Stein.
My area of research is in analytic and algebraic number theory; specifically, my dissertation focuses on theorems and methods surrounding the lowest nontrivial noncentral zero for elliptic curve L-functions, and how these can be used to modify existing analytic rank estimation methods to make them fully explicit with known complexity in the curve's conductor. I'd like to include computational results in my dissertation, so having an implementation in Sage of a full analytic rank algorithm is a natural step. One way to slay multiple birds with one stone would be for me to do just that as a Google Summer of Code project. Current analytic rank methods available in sage all call external libraries, only provide rank upper bounds, and scale at best in polynomial time with regards to the conductor, which limits their effectiveness. However, Jonathan Bober, currently at the University of Bristol, has written some highly efficient analytic rank bounding code in c and cython for psage that scales much better with the curve's conductor. For example, he has used it to show that Elkies' rank 28 curve has analytic rank at most 28*. I would like to port this code over to the main sage library, and in the process clean it up, document it fully and modify it appropriately so that it computes analytic rank exactly (assuming standard conjectures). This will require a significant amount of new code to be written, which in turn necessitates good knowledge in both analytic number theory and sage development. My proposition is to work on this project under the co-mentorship of Jonathan Bober and William Stein. Jonathan is not a registered mentor for sage-gsoc; I have approached him separately with this request. However, I believe the project is structured well enough already that I could also complete it under another mentor with good knowledge of elliptic curves, such as Jean-Pierre Flori. I believe that I'm well placed skill-wise to work on such a project. I have five years experience with Sage, both at the user level and from an architectural viewpoint - in the course of my graduate studies I've written and reviewed numerous patches for sage, and I have contributed to code at a number of Sage Days workshops. My experience is mostly with Python, but I have a decent amount of exposure to Cython. And because of my research I have the mathematical knowledge necessary to work on such a project. Please let me know if such a subject would be of interest to the sage-gsoc team. I look forward to a summer of code! Regards Simon Spicer University of Washington *Bober's original paper showed that Elkies' curve had analytic rank at most 28 or 30; this bound was subsequently lowered to 28 as a result of a computation by Jamie Weigandt at Purdue. -- You received this message because you are subscribed to the Google Groups "sage-gsoc" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at http://groups.google.com/group/sage-gsoc. For more options, visit https://groups.google.com/groups/opt_out.
